The default size of INTEGER variables remains unchanged (2^31-1), so INTEGER*8 (8-byte) variables must be used to index extremely large arrays. These variables are implemented in a more efficient and natural way in 64-bits. Note that some arrays that would not fit in the old 4GB limit may still be indexable using default sized integers, for example a REAL*8 array of 2,000,000,000 elements would occupy nearly 16GB of memory, but could be indexed using default integers.

2 billion elements seems like 'extremely large' , to me snywsy.

Given that the vast majority of consumer PC's are still xlowly moving from 4Gb to 8Gb physical memory, even 16Gb is out of range for most people, and even most companies in my experience as they tend to lag well behind in terms of hardware spec)
So, my question is, how does one get the 16 Gb of memory (or more for 64-bit) without mortgaging your house !?!?!
I assume it would be 'paging' (virtual) memory, but how would that be implemented ?

If you look at the post on "Some issues with roundoff and a whole lot else", I looked at the memory capacities for self-build computer components, and most mainboards support 32Gb, but you can, for a price, get 8-socket boards with correspondingly expensive memory. My prices are in GBP.

Just about everything I want to do can be done in 1Gb, but I recognize the need of folks like Dan and John in Oz to access all the RAM they can. It seems to me that a 1D array or REAL*8 could take up 16 Gb with 2Gb elements of 8 bytes, let alone 2 or 3D arrays.

The fact that bigger than 4-byte indexing is needed in terms of bytes doesn't seem to me to need bigger than 4-byte integers for the variables. But hey, it's all academic in the sense that I'll never need to use it.

John, Ask your own or any 10 years old kid in the world do they want GTX 1080ti with 11GB of RAM or not. They will ask you if you can buy two. Or three. And will perfectly explain and demonstrate why even more RAM is needed.

Same but often much worse with our modeling. The modeling world is even not 3D but more multidimensional. Remember that Fortran 77 had 7-dimensional restriction ? I suffered from that because for one task i needed 8.

With plasma PIC codes for example you need for ions 3 space dimensions, 3 momentum dimensions, 1 more for ionization state and 1 for partitioning. And that for 2-3 different elements. Total 9. Total 7 dimensions needed for electrons (they all have ionization =1). Also data needed for the EM fields: 3 for electric field, 3 for magnetic field. Do the math how many particles you can include in the simulation for realistic modeling.

all this is all well and good, but many folks can'rýt afford 32Gb memory computers, and for laptops that limit is much less too.
I read when SSD's came into prominence 2 or 3 (or maybe 4) years ago that one application of them was to use for extra 'memory' but I never found any article which explaind clearly and smply how that works .
Hence my question about virtual (paging) memory.